13. 3 5 4 10 1 1 2 1

Q: Find the rank of the following matrices.

A:

Q: In Exercises 11-16, compute the adjugate of the given matrix, and then use Theorem 8 to give the…

A:

Q: NA 1.2) Consider the following new task: 101) Suppose the "N" on the left is written in regular 12-…

A: Step 1: Step 2: Step 3: Step 4:

Q: 6. Prove that if A is invertible and AB = 0, then B = 0.

A: Given that A is an invertible matrix (obviously A is a square matrix), i.e. A−1 exists.We now prove…

Q: Find all matrices A = (a,b;c,d) that satisfy A(1,1;1,1) = (1,1;1,1)A

A:

Q: 20) Find the conditions on a and d such that the matrix A = [] has and inverse. What is the inverse…

A: Given,

Q: 8 Consider a square matrix B whose inverse is given by B'. a In terms of B", what is the inverse of…

A:

Q: 6. 1 -5 -4 0 3 4 -3 6 0

A:

Q: 3 5 4

A: Theorem 8: An Inverse Formula  "Let be an invertible matrix. Then Adjugate Matrix: Let be an…

Q: 7. x1 4 -1 7 -4 + x2 -5 3 -5 1 + x3 7 -8 0 2 = 6 -8 0 -7

A:

Q: Find the inverses of the matrices in Exercises 1-4. 1. 8 3 [5 2

A:

Q: b) Let A, B, and C be nxn matrices and suppose that ABC is invertible. Which of A, B, and C are…

A:

Q: 15. -1 1 0 -2 3 -1

A: A=500-110-23-1

Q: 0 0 1 -1 0 0 -1 2002

A:

Q: In Exercises 19–20, solve the matrix equation for X. 1 1 2 -1 5 7 8 - 19. 2 3 0 | X = 4 -3 1 2 -1 -7…

A: To find X

Q: [ 8 }] -7 -3

A:

Q: Consider the matrices in Exercises 1–10. a) Either state that the matrix is in echelon form or use…

A:

Q: Show that if a matrix A has an inverse A-, then in fact A-1 has an inverse as well

A:

Q: In Exercises 11 and 12, use an inverse matrix to find [x] for the given x and B 11. 3 -4 = = {[³]…

A:

Q: 47. Prove that if A and B are square matrices and AB is invertible, then both A and B are…

A:

Q: Show that a matrix B has a left inverse if and only if BT has a right inverse.

A: Let’s assume that C is a left inverse of matrix B i.e.